Is there a reference with the list of maximal subgroups of SU(p,q) for "small" values of p and q? (such as SU(3,1) as suggested in the title of the question)
Mohamed Selim Taufik, On maximal subalgebras in classical real Lie algebras: "This paper is concerned with the classification of irreducible maximal subalgebras of the classical real Lie algebras su(p,q), sv(p,q) and si(p,q). We use the results of E. B. Dynkin, who classified the maximal subalgebras of the classical Lie algebras in the complex case. (...)" Boris P. Komrakov Maximal subalgebras of real Lie algebras and a problem of Sophus Lie: "A classification of the maximal proper subalgebras of the simple real finitedimensional Lie algebras is presented without proof. Contributions by A. A. Morozov, E. B. Dynkin, M. Berger and M. S. Taufik are mentioned." 

